mn-^^ ^
ACE No. IAH21
S^
n
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
WARTIME REPORT
ORIGINALLY ISSUED
August 19*+^ as
Adyance Ccaafldentlal Report IAH21
THE EFFECTS OF EOIXJHKESS AT HIGH REIHOLDS NUMBEI^
ON THE LIFT AND IRAG CHARACTERISTICS
OF THFtEE THICK AIRFOIIS
By Frank T. Ab"bott, Jr. and Harold R. Turner, Jr.
Langley Memnrlal Aeronautical Lalioratory
Laneley Field, Va.
''teSSSr.'SK'riKlfP
NACA
WASHINGTON
NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.
L . i;6 DOCUMENTS OEPARTMFN"
NACA ACR No. 1J4H2I
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ADVANCE CONFIDENTIAL REPORT
THE EFFECTS OF ROUGHJIESS AT HIGH REYlv'OLDS NUMBERS
Oil THE LIFT AND DRAG CHARACTERISTICS
OF THREE THICI-: AIRFOILS
By Frank T. Abbott, Jr. and Harold R. Turner, Jr.
SUMMRY
In connection with studies of airfoils applicable
to largo high-speed aircraft, the effects of roughness
on three 22-percent-thick airfoils were investigated.
The tests were made over a r--.nge of Re.7nold3 nu;nber from
about 6 to 26 X 136 for the airfoils s;!incth and with
roughness strips applied to the surfaces. The results
indicated that for the roughened iriodels the scale effect
Was generall" favorable.
INTRODTTCTION
Previous tests in the NACA two-dimensional low-
turbulence pressure tunnel of thick airfoils with
roughened leading edges (reference 1) indicated that
the lift and drag characteristics of the thicker wing
sections, when accidentally roughened, would have an
important bearing on the choice of sections for large
high-speed airplanes. These tests were limited to
Re'molds numbers much lower than the flight values for
such airplanes hj the use of 2-foot-chord wooden models.
The desirability of extending the tests to higher
values of the Reynolds number was apparent, and an air-
craft manufacturer submitted three J-foot-cliord models
of heavy metal construction for this purpose. The three
airfoil' sections v;ere: an NACA 63 (Ij.20)-Il22 -airfoil; an
NACA 65(223 ) -1^22, a = 1,0 (anprox.) airfoil, where
"(arprox,)" refers to a slight thickening near the
trailing edge; and a 22-percent-thick Davis airfoil.
These models were tested in the NACA two-dimensional
low- turbulence -Dressure tunnel in order to obtain lift
CONFIDENTIAL MCA ACR No. iJ^HZl
and drag characteristics at Reynolds numbers up to approxi-
mately 26 X 10° v;ith smooth surfaces, with roughness
grains of various sizes on the leading edges, and in
some cases with roughness strips at various chordwise
positions.
TEST METHODS
All tests were conducted in the NACA two-dhnensional
low-turbulence pressure tia:inel, which is characterized
by an air stream of extremely lev/ turbulence. The models
extended from wall to v/all of the rectangular ter.t sec-
tion. Lift measurements were obtained by a manometer
arrangement that integrated the lift reaction of the
models on the floor and ceiling of the tunnel, and drag
measurements were m^ade by the wake-survey method (refer-
ence 2). A correction of aboi;t 2 percent v/as applied to
the data for normal t\mnel-wall-constriction effects.
Lift coefficients near m.aximum lift v;ere further corrected
for additional t'onnel blocking that occurs v/hen the model
is partially stalled. These additional corrections,
derived from static-pressure mieasurements made along the
floor and ceiling of the tumnel, varied from to about
10 percent. Tests were m.ade at tunnel tank pressures
from 50 pounds per square inch to I50 poijinds per square
inch and, at all times, the tunnel airspeed was low
enough to avoid compressibility effects.
The airfoils submitted by the aircraft manufacturer
had 56-inch chords, were of heavy metal construction, and
were painted to give aerodynamlcally smooth surfaces.
The two low-drag airfoils were tested first smooth, then
with various sizes of roughness on the leading edge, and
finally with 0.011 -inch roughness grains at one or more
chordv/ise positions. The Davis airfoil was tested smooth
and with roughness grains of two sizes on the leading edge.
Tests were made of all three models, both smooth
and rough, at Reynolds niimbers of approximately 6, 10,
1I+, 20, and 26 x 10^.
The roughness sizes of 0.002, O.OCli., and 0.011 inch
represent the average size of the carborundimi grains
used. The roughness was applied to the leading edge
CONFIDENTIAL
NACA ACR No. rJ+H21 CONFIDENTIAL
by coating a strip fro?n 5. 50 to 5 '75 inches wide, sym.-
raetrically spaced about the chord line at the leadirg
edge, with thinned shellac and sprinkling with carbo-
rmidutn grains until 5 to 10 percent of the area was
covered v/ith grains. The roughness strips at 20 percent
and 50 percent of the airfoil chord (0.2Cc and 0.5Cc)
were similarly applied b^it were 0.5 inch wide wibh the
forward edge of the strip at the specified chordwise
location.
RESULTG AND DISCUSSION
NACA 63(1;.20 )-!,22 Airfoil
The effects on the lift and drag characteristics of
four sizes of roughness applied to the leading edge of
the NACA 65 (l!-20 )-li.22 airfoil section at a Re^^molds number
of 26 X 10° are shown in figure 1. Tb.e loss in maxirnum
lift tended to be gradual with increasing roughness size,
but the increase in drag coefficient in the low-drag
range was not gradual. The application of shellac alone
to the leading edge caused a large increase in drag coef-
ficient in this range. The shellac, however, did not
decrease the lift coefficient at which the drag increased
sharply to extremely high values, whereas all other
roughness sizes on the leading edge did.
The effects of the 0. Oil-inch-grain roughness at
various chordwise positions are shown in figure 2. There
was no large detrimental effect on maximum lift •'onless
the rough_ness was on the leading edge. This result is
attributed to the fact that at ma:-cimum lift the shape of
the pressure distribution causes transition on the upper
surface to occur close to the leading edge. The effect
of roughness, therefore, in the thick turbulent boundary
layer downstream of the pressure peak would be expected
to be small in comparison with the effect of roughness
in the relatively thin boundary layer at the leading
edge. The drag coefficients at low and moderate lift
coefficients increased as the roughness was moved toward
the leading edge, as _ would be expected from the accom-
panying forv/ard movement of transition. The roughness
strips at 0.20c and 0.50c, however, did not appreciably
affect the value of the lift coefficient at which the
drag increased to extremely high values. At these
CONFIDENTIAL
k CONPTDENTIAL NACA ACR No. li4.H21
locations, the boundary layer cannot be laminar at such
lift coefficients because of the shape cf the pressure
distributions.
The scale effect on the lift and drag characteristics
of three sizes of roughness on the leading edge Is shown
in figures 3 to 5« These plots show, in general, a
gradual decrease in drag and an increase in raaxlmiim lift
Y/lth increasing Re},Tiolds number - that is, the scale effect
was considered favorable - for all three sizes of roughness.
NACA 65(223)-l|22 (Modified) Airfoil
Lift and drag characteristics of the NACA 65 (225 )-Ii.22
(modified) airfoil are sho\vn in figure 6 for four model
conditions; namely, 0.00l4.-inch-graln roughness on the
leading edge, 0. Oil -inch- grain roughness on the leading
edge, 0.011-inch-graln roughness at O.JOc, and smooth at
Reynolds numbers of ll^. and 26 x 10°, The curves for the
model in a sm.ooth condition are presented to show that
this section had a gradual Increase in drag Vi^ith increasing
Reynolds number - that is, the scale effect was con-
sidered adverse - in the low-drag range. This result
was probably caused by some slight surface irregularity'-
v/hich, because of the small slopes of the favorable pres-
sure gradients of this section, make it unusually sensi-
tive to any surface defects and lonfairness. It is thought
that lower drags than are shown for this section are
possible, but NACA 65-serles airfoils (reference 2) which
are preferable to the one tested are now available.
The application of roughness to the leading edge of
the NACA 65 (223 )-l4.22 (modified) airfoil seriously
decreased the maximum lift and caixsed a large decrease
in the lift coefficient at which the drag increased
rapidly. The greater part of the drag increment attri-
buted to the roughness grains was caused by the smallest
roujjhness size tested. The roughness strip at 0.30c did
not affect the maximum lift coefficient to any great
extent, because the flow over the top surface of the
airfoil at this high positive angle of attack had become
turbulent much nearer the leading edge.
The effects of 0.00i|-lnch-grain and 0.011-inch-
graln rouglmesses applied to the leading edge at
Reynolds numbers from 6 to 26 >: 10° are shown in fig-
ures 7 3ind 8, respectively. The scale effect was
CONFIDENTIAL
TAG A ACR JIo. r4H21 CONFIDENTIAL
generall:,'" favorabl9, especially in the case of the
drag coefficients, hut became \^ery small at Re;^,'nolds
mxmbers of 20 to 26 x 10". The increase with Reynolds
mxnber- of the value of the lift coefficient at v/hich
the drag coefficient increased sharply v/as especially
notable .
Davis Airfcil
Lift and drag data for the Davis airfoil in the
smooth condition and v/ith 0.002-inch"grain and 0.011-inch-
grain roughnesses applied to the leading edge are pre-
sented in figiire 9« A comparison of the lift and drag
curves obtained for the smooth model with the curves
obtained with roughness on the model shows that even the
smaller (0.002-inch grain) rouglmess caused a loss in
maxlmuin lift coefficient of arjproximately 0.1\., a slight
decrease ^n lift-curve slope, and a large increase in
drag throughout the range tested.
Results ol' tests wltb roughness grains of 0.002
and 0.011 inch on the leading edge at Reynolds numbers
from 6 to 26 x IQ'^ are presented in figures 10 and 11,
respectively. Scale effect on the drag coefficients
was favorable for both sizes of roughness by.t became
small at Reynolds numbers of 20 and 26 x 10'='. There
was a small favorable scale effect on the maximum-lift
valTies up to Re^molds numbers of 20 x 10*^ and small
adverse scale effect for both sizes of roughness at
Reynolds numbers from 20 to 26 x 10°,
COMPARISON OP AIRFOIL SECTIONS
The drag coefficients of the NACA 63(L23)-1|22
airfoil section and the NACA 65 (225 )-i+.22 (modified)
airfoil section vvlth roughness stri-os of 0.011-inch
■^o
grain at O.JOc are compared in figure 12. In this
condition the extent of the laminar boundary layer
should be the same for both sections at lift coeffi-
cients corresponding to the lov/-drag range for the
smooth airfoils. The drag coefficients were nearly
the sajne for lift coefficients below about' 1.2; the
differences shown are not considered greater than
GONPIDENTI^.L
f
COin^IDEITTIAL NACA ACR ITo . iJ+HZl
_ ossible variations for teats with roughness. Pig-
v.ve 13 shows a similar conparison for the three airfoils
tested with 0.011-inch-grain roughness on the loading
edges. The NACA G3 ih-^-O ) -l\.2Z section was more resistant
to separ'aticn when ro^Agh than the other two sections;
that is, the lift coefficient at T,i'hlch the drag coeffi-
cients rise sharply to very high values vms appreciably
higher for this section than for the other sections
tested. Numerous spanwise drag surveys ".vere made of
the tliree models with roughnesj on the leading edges.
These surveys showed that the HACA 63(ij-20)-I{-22 airfoil
had no localized separation v.p to moderately high lift
coefficients, that the XACa 65 (223 )-422 (.aodified) air-
foil sho'ved marked local separacion at much lower lift
coefficients, and that the Davis airfoil showed local
separation at lift coefficients above approximately 0.8.
The Gffects on the drag coefficient at a lift coef-
ficient of O.L|. of various sizes of roughness on the
leading ddge for the three airfoils tested are shown in
figure ll|.» All throo airfoils had nearly the same drag
coefficient whe:i rough and the drag increased very
little with increasing rou.ghn3S3 size, A large increase
occux'red, however, from the s-nooth condition to the
smallest size of I'ougxir.ess .
Both the NACA low-drag airfoils were affected
by rougimesr less at the high Reynolds mx'n.bcrs than
at the lov/er Reynolds numbers. This favorable scale
effect v;ith the models in a rough coxadltion increased
the lift coefficients at which the drag coefficients
increased rapidly to extremely high values by nearly 0.I4.
for the NA0A"65(225)-ii-22 (modified) section and 0,2' for
tb.-e >LvCA •j3(l+20)-i|.22 section. The Davis airfoil shov/ed
practically no favorable scale effect in this respect
although th^^ effect on drag coefficient at lower lift
coefficients was favorable.
CONCLUSIONS
Tests of an NACA 65('.|.20)-)^22 airfoil, an
NACA 65(225 )-I|.22 (modified) airfoil, and a 22-percent-
thlck Davis airfoil, all with roughness strips on the
surfaces, indicated the following conclusions:
1, In genera]-., the airfoils with rougliiiess strips
shov/ed favorable scale effects over the Re^Tiolds number
CONFIDENTIAL
NACA ACR No. LI4.H2I G0NFID3ITTIAL 7
range from 6 to 26 x 10°, This favorable scale effect
was particularly effective on the MCA airfoils in
increasing the lift cooff Icients at which the drag
coefficleats increased sharply to very high values.
2. At sraall and moderate lift coefficients, the
drag coefficients for all the sections tested ;vith
leading edges rough were nearly the sajne for the same
roughness condition and Reynolds nuxrJoer, With roxigh-
nsss strips at 5^ percent of the chord, the drag charac-
teristics of the tv.'o NACA airfoils tested v;ere nearly
the sanio except at the highest lift coefficient.
5. Increasing the size of the routv;hiness grains
applied to the leading edge pi'ogressively decreased
the raaxir;:ura lift coefficients for the sizes tested,
but the greater oart of the drag increment caused by
the roughness occurred with the sr.iallest roughness tested,
i}.. The order of merit of the three airfoils in
pemitting high lift coefficients to be obtained without
excessively high drag coefficients with the leading edges
rough is as follows: the NACA 65 (i|.20) -14.22 airfoil, the
NACA 65 { 225 ) -[(.22 (modified) airfoil, and the 22-percent-
thick Davis airfoil.
5. The naximum lift coefficients of the NACA air-
foils tested were not affected to any great extent by
roughness strips at 20 or JO percent of the chord back
of the leading edge.
Langlejr T.femorial Aeronautical Laboratory
National Advisory Goir!:nittse for Aeronautics
Langley Field, Va.
REPZR3NGES
to Separation. N/'GA G3, June l'^k.2.
2, Abbott, Ira E., von Doenhoff, Albert E., and Stivers,
Louis 3,, Jr.: Sur3Vlar^^ of Airfoil Data. NACA AGR
No. L5CO5, l'9kb-
GOlfPIDENTIAL
Digitized by tlie Internet Arcliive
in 2011 witli funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation
•
http://www.arGhive.org/details/effectsofroughneOOIang
NACA ACR No. L4H21
Fig. 1
►J
O
O
<
Q
O
1^2
O O O
• • •
I f
\K
B
Ol
(>4
^>
)
1 CM
7. 9
•• X
^ ^0 •• ••
O ry fl ■
t> o ■
/
^
n;^
^
1m
^
"b«<
^^
■""t
^d
^^
■S
%
f^
^«r
u
cvj
00 -2
s
'9 'ao*T0tjjao9 ajtl uoi40*G
NACA ACR No. L4H21
Fig.
<
E-<
Z
Ed
O
I — I
O
O
0.
(0 g
(0 •
. «o
Mai
1
^
u
B
t» c
too
\
?f
■>
Si
+ —
1
if
^
d
K
" O "
u o
t =
s
<
-o-^
"^^^
n
\
;-^
00
o
s
k.
V
N
H
\^
\
\^
\
^
+
b
is
+
1
\\
y
■So
//
I
1^
/
/l
J
1
\
/
/
J
/
J
l>
y
A
V
0--
^^n
/
r,
^
y
o
o
o
GO
nl w rH
o o o
39
s
1
^
|r
;
1
o
< .ir>
o c ir*
z o
iHvo e-«
.. x-^e
-^ vo ••
O t\J -o -
N,
V
p
K
Hl^
^
3Kil
■*^
■a^
:ar?i,.
^
^
"^
n
R^
1
>
H -o
=?!
Z
Cd
Q
O
O
3
1h «
■H d
4 o
CM •a
r o
o
OJ ©
-T CO
^--^
eg
1o 'naeiofjjeoo ^Jti uo-n»»s
NACA ACR No. L4H21
Fig,
<
Q
O
O
.
|l
N.O 0_4-0\0
0+ XQO
■1^
li
^
cvi
50
y
/ /
■'/
1
S
rN
VsV
\
\t
\
%
T
J
n
li
)l
m
^
^
■
1
r
1
?
>
n
H
C
[
>
a
3
i
s
'
<
S
\
s
3
9
1
1
r
e
's '^u'Toijjsoo i«,ip nox^ots
-^
N
O
c3
.J
<
t— 1
El
2
vO
U
rH
o
1 — 1
fe.
•4
2
O
o
Pf
>
J
Y
!
o
••
rH
£ tZ
u o ■
-H XI »
< Of*
1
1
\
^
f>«.
^^
**.
Vln
N,
^
^
r^
r^
s.
I
G-
—
^
s
a
•4
O
t .
%^
n
« ■
31
■ «
o
•4 s
«• ■
■ !
w
«
to
5
%
» '»a9TOWJ»oo ijii uoii9»s
NACA ACR No. L4H21
Fig.
<
Q
I— t
o
o o o
'0 '4U»X0.[JJ»00 9»jp D0^}09S
C\J
)
1
o
_ ^e
o -o -
Vt t< -P
h on
ii
'
w
V
^
>»
N*
^
N
s
N
V
^
^
^
J
(T '^
■a
to
•a
9
►J
<
El
Z
Q
O
U
5
« to
CM*
la
Old
-c3
ViiH
O O,
i
»» 3
o o
cow
§4
'o '^ueioTjjaoo ;(jti ao^ioes
NACA ACR No. L4H21
Fig.
Q
O
S
£ 1
r-i
PS X
so O-d-OsO
S "*
p
1
* =
"
<i^
^TC
^" j"i \
!«,
■■ u
-ftL
>^
N
N
^^
^
\
~\^
i.
h\^
\
)
\
X
I
W
T
^—i
^
o^
'S^
^
,*^
(r^
»1
-^5
O q
o
o
eo
3
o
<
El
W
Q
O
O
5
o
%<^
X "
10
VlH
o a
a
(A Id
■^t '«B*Tot«j«eo Stop uoi^oas
J
^^
%
in
:?8
#
O
(j
^
^
3
^
V,
-^«J
'^
Sir
AlrfoH
Chord:
Test:
^
^
1
K
— 1
^
\
%
X
P
0"
T?
^«
<?!
W 00 _:J Ci _aT
O I
NACA ACR No. L4H21
Fig,
I— I
E-i
Cz]
a
o
o
fi
I
li
1 o
O <a
=: (0
O Jh
■^
u
o
C«^
•-< -
so
u n
C a
^.5
o a
• o
o u
+
tec
o «
C n
O 3
- O
O u
o
is
s
c —
o
1-
O
X
O
o
■«
+— -.ii---.
/
'^v-i.
5~^
/
/
3
-^^ "^
^
^1 ^
kj^
C-^^ '
\
\
K^
r
\
1
J
u
1
•1-
rr
!
l\
(
Ml
'/)
''y^
A
/.
/
C
"://
V
f
^
+
1
1 ! 1
<
z
Ed
o
o
] N C4 ri
o o o
o
o
1
1
■o
ol
^
CM
-f
Oi
w -a
;;; 5
U CC\J
•- X
— t sC •• ••
o oj -o «
t, O o
\
p:
r
^
\
^
^
w
^
l^d
n
•y
^
^L
"^
^
~
\,
^
s
^
^
1 1 1
-^ «
t* >
3] ■-<
t< ft
o
to
I
b '»u»i3xjj8oa ijfz U0HS9S
NACA ACR No. L4H21
Fig,
<
Ed
a
o
o >«
CM 1-1 r
O O c
p A
>o
%
£»^
1
OJ
-*
OJ
OJ
in
-< Mn
O flOJ
H
£ ^i-
(h O (D
tH ^ ©
•< Of*
^
«i*
iti
"^
k
V
^ti
^
-->£
1
s
%
^
^
^<-h
i
^
OJ
.<e
<
W
O
I — I
Cr.
2:
o
o
-I
in ♦»
M5
O -H
5-3
o a
*^
a) I
<o -*
■d O
OS ^
^.
'o '^ue^OTjjeoo »jtt uo^oes
NACA ACR No. L4H21
Fig. 8
O
O
i
Si
KX
^O O_d-0s0
rHHty eg
+KG10
1 ' ' '
^2
ii
^
B— ^
ih
1
— ^
hh
fe
7-^
^
6-
■-N
^
•^
\
^
^
\
l^\
\
m
%
r
/a
, Q
^
V
r
o-
■t
:^
d
^
€
^
■^
g
f
Q
O
O
CO s
C V
"At
o U)
a a
-^
eg 4
<■%
OH
a
d ai
s 'tu^-tOTjjvoo 8«ap act^osB
!»
%
<
1
CM
o onl
L
w
^
w
^
nq
N»
'^
s
"n-
o o -
^ h -P
U OK
>
\
f
^
6
so -0
HO
9
o a
ft
tjo'
9.4
1
to
,^
*o '^uejo^jjeoo »jTt uc-j»obs
NACA ACR No. L4H21
Fig. 9
<
I— I
c-<
Q
O
C W
a
1 o
u n
O 3
X
—
fee
u «
C ■]
' o
o t,
+
u
—
— **
o
o
-a
G
li
!§
11
^4
s
I
V
\
\
\
I'
^
. .
IV i
^
\
X
\
\
\\
c
/
o
A
/
i
/
/
J
,^
y
/
f
U-
-^
/
/
/
^'
J
o
^
^0 '^aQTOTJiOOo 8wap uo^tioes
H to
OS -d
«>
<jO
^ t£
> C
a] -H
U i-l
f3
O TJ
«>
OS -H
O CO
*3 ^
O CO
03 <D
a «
o
p
H
£ S
» X
o c\J TJ m
t. O «
^ ••£ e
J
•4
■
n
i
1
n
^
^
Sjj
^
^
X
^
'O^
X)
—
♦J
I
3>
►J
<
Q
O
'^uejOTJjooo jjTx uo^iass
NACA ACR No. L4H21
Fig. 10
<
O
O
o
P
li
SO 0_40vO
+ X D O
_ o
fe
3
i — .
"^
/
vn^
^^
^
N
L/^\
St H
^>
1"
lA
/
/<
rr^
i^
tr<!(
°^
€
W OJ rH r-
O O O C
'jueTOTJjeoa Ssjp uo^^aag
O
iH
O iTv
cy -3-
o c
iH -O
> C KN
O -On
f. O CO
»< a v
<
\A
:^
^
VJj
\
^
K
%
N.
%
Si
s
K
N
lo
00 n
t-1
Cd
Q
I— t
Cr,
z
o
o
(0 t]0
> «
3^
I
*-. o
■MO
•aa»T3TJJ»03 5JTT uof^oes
NACA ACR No. L4H21
Fig. 11
<;
Q
o
o
Q ^
_»
^0
\D O_a-0v0
«H ^ CM OJ
s
-*i
/ /
/
!/
'
k
r^
?^
^
^^
h
N
^
t
V
1
ik
y
/
/
^
r^
^
,_
t
V
?
r
g
a
>
t
c
>
^J
f
o^
^o '^usxSTJjaoo 8*.ip uof^oas
i4
-^
OJ ^
• tJ
G
— to
CO
> ^-0
Q H
rH
^ CO
■H j:: a>
ft
X
7
^
Si
%J
^
^
\„
1
^.
k
s
2;
Ed
Q
O
O
> q}
4^ fi
OJ
OJ
S
4J
00
a.
n,
-4
to
01
4H
a>
t.
a>
(U
a
4J
ft
(rt
1
t^
3
I.
c
ti (rt
^'
te
Jl
Tl
f)
c:
at
-H
*J
rH
u
rH
J
•
to
'o '^ueio^jjeoo ajTI uo^oss
NACA ACR No. L4H21
Figs. 12,13
<
I — I
E-i
w
Q
O
S
-x,
|i
K
«
H
^
k
h
n
Y
_, £
3 '^
o
T3
O
1
a
\
X
\0 -
1
s-
/^
f
<
O
4-
^
^
1
t'^
b<^
•p
\
< — -
?
<^
o
o
O «0 (M
CM i-l .H
O O O
o a;
(D <D
+3 o
CO S
. I
lO r-l
r4rH
o
ll> .
tiO
V^
3
+
5^,
1°
\
_» o
1?"
\
ii
t)
'\
k
s
\
o
\
T
fV
CM
cy
^ _
C\J
f\J
<
O
+
OJ
i
tc
o
t
T
<
/7
o
4,
T
'^-;
f
c/
o
Vi 3
o o
U 1
0) ^
*^ o
t) a
« -H
ti 1
a r-i
Xi r-l
oo
too
a]
bxl
Q«=
^
CO
o
o
o '1U910TJJ800 Sbjp uo-noes
NACA ACR No. L4H21
Fig. 14
<
I — I
z
Cd
Q
I— I
tr.
O
O
1
r^f*
^
o
•H
O
g
\ ^
•H
n
o
s
1 s
' OS
c\i
rvj
CM
OJ
«
3
C
F
! LL.
'
CO
1
:
'
>
Q
iH
X
SO
rvi
••
S-5 -
/
/
1 / V
/
f
C
— s
c
-
:>
c
- /
1^ .-'
"T< r-
1
D
i
X. .^ _
W
— >
-o*-
vC
CVJ
GO
O
o
o
o
P© 'i^uofOfjjaoo 3»ap uoft^oas
s ^
'Cj l-H
© E-.
«) g
C Q
*H ^
XJ (i.
«J 2
« O
H u
C
o
J^
o
o
(4
•
•H
(0
C
*<
o
tf
H
»<
o
bO
• •
c
(0
•H
n
0)
GO 01
.§
o q
o ^
• ca
O B
&,
V( O
_ n
o ^
.00
ghne
o
3
n o
O
-5
O -P
O o
V^
*
43 O
«
d
M
•H
S"
o
O
•
c
o
a
■p
o
o
a>
V4
^
1
•
^
9
l[/NIVERSITY OF FLORIDA
262 08104 979 2
UNIVERSITY OF FLORIDA
DOCUMENTS DERARTME.^^
GAINESVILLE. FL 32611-7011 USA
TVNews
OpenLibrary